Tuesday, January 21, 2014

Utility and the infinite multiverse

If we live in an infinite universe, then when we look at total values and disvalues, total utilities, we will always run into infinities. There will be infinitely many persons, of whom infinitely many will provide instances of flourishing, after all. Now one might say: "So what? Our individual actions only affect a finite portion of that infinite sea of value and disvalue."

But this may be mistaken. For if there are infinitely many persons, presumably there are infinitely many persons who have a rational and morally upright generally benevolent desire. A generally benevolent desire is a distributive desire for each person to flourish. It is not just a desire that the proposition <Everyone flourishes> be true, but a desire in regard to each person, that that person flourish, though the desire may be put in general terms because of course we can't expect people to know who the existent persons are.

Now, if you have a rational and morally upright desire, then you are better off to the extent that this desire is satisfied (some people will think this is true even with "and morally upright" omitted). Thus, if you have a rational and morally upright general benevolence, then even if some men are islands, you are not. Whenever someone comes to be better off, you come to be better off, and whenever someone comes to be worse off, you come to be worse off. So if infinitely many people have a rational and morally upright general benevolence, whenever I directly do something good or bad to you, I thereby benefit or harm infinitely many people. And no matter how small the benefit or harm to each of these generally benevolent people, it surely adds up to infinity.

St. Anselm thought that our sins were infinitely bad as they were offenses against an infinite God. If we live in a multiverse, those of our sins that harm people also harm infinitely many people.

One might object that the generally benevolent person will only be infinitesimally benefitted or harmed by a finite harm to one person in the infinite sea of persons in the multiverse. That may be true of some very weakly benevolent people. But there will also be infinitely many generally benevolent people whose general benevolence will be sufficiently strong that the benefit or harm will be non-infinitesimal. After all, one can imagine a person who, if faced with a choice whether she should gain a dollar or a stranger she knows nothing about should gain a hundred dollars would always prefer the latter option. Such a person counts benefits and harms to other people at at least 1/100th of what such benefits and harms to herself would count as. And so if I deprive anybody of a hundred dollars, each such a generally benevolent person will, in effect, be harmed to a degree equal to a one dollar deprivation. As long as there are infinitely many generally benevolent people with at least that 1:100 preference ratio, the argument will yield that a non-infinitesimal harm to anybody results in an infinite harm. And plausibly there would in fact be infinitely many people with a 1:1 preference ratio, or maybe even a 2:1 preference ratio (they would rather that others benefit than themselves).

So we cannot avoid dealing infinite utilities if there are infinitely many persons. For each of our nontrivial actions will affect infinitely many persons, since infinitely many persons will have rational and morally upright desires that bear on the action.

Moreover, even denying the existence of an infinite multiverse, or of an infinite universe, won't get us off the hook. For even if we don't think such an infinitary hypothesis is true, we surely assign non-zero epistemic probability to it. The arguments against the hypothesis may be strong but are not so strong as to make us assign zero or infinitesimal probability to it. And a non-zero non-infinitesimal probability of an infinite good still has infinite expected utility.

Interestingly, too, as long as overall people flourish across an infinite multiverse, each such non-infinitesimally generally benevolent person will seem to be infinitely well off. Such are the blessings of benevolence in an overall good universe.

The above argument will be undercut if we think that one only benefits from the fulfillment of a desire when one is aware of that fulfillment. But that view is mistaken. An author who wrote a good book is well off for being liked even if she does not know that she is liked.

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I am a philosopher at Baylor University. This blog, however, does not purport to express in any way the opinions of Baylor University. Amateur science and technology work should not be taken to be approved by Baylor University. Use all information at your own risk.